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We consider a stochastic model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows in a network where bandwidth is…
We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha>0$) proposed by Roberts and Massouli\'{e} [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that…
We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal…
Bandwidth-sharing networks as introduced by Massouli\'e & Roberts (1998) model the dynamic interaction among an evolving population of elastic flows competing for several links. With policies based on optimization procedures, such models…
We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network. We study weighted proportionally fair sharing policies and establish explicit-form bounds…
We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies…
Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…
There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by…
A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
In previous papers we developed a deterministic fluid approximation for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…
The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs…
We consider a multihop wireless system. There are multiple source-destination pairs. The data from a source may have to pass through multiple nodes. We obtain a channel scheduling policy which can guarantee end-to-end mean delay for the…
We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance…
Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Recently, several authors have shown that the invariant distribution of such networks admits a product…
In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We study load balancing under the Batch Sampling routing scheme for a network of $n$ servers storing a set of files using the…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…
We consider a multi-hop switched network operating under a Max-Weight (MW) scheduling policy, and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the…
Since its inception, control of data congestion on the Internet has been based on stochastic models. One of the first such models was Random Early Detection. Later, this model was reformulated as a dynamical system, with the average queue…